The method of measuring the speed of light was first proposed by Ole Roemer around 1676, by measuring the distance/interval of Jupiter’s eclipse over Io. Io is one of about 79 moons orbiting Jupiter — Io belongs to the Galilean moon group along with Europa, Ganymede, and Callisto. Roemer himself was a Danish scientist who at that time worked at the Paris Observatory.
The idea of using Jupiter’s moons as natural “clocks” is not really new, as Galileo Galilei had proposed some time before Roemer’s observations. Nevertheless, Roemer managed to make a step forward rather than just using the months earlier as a “clock”; he used it to measure the speed of light.
The story is, after carrying out years of observation, Roemer found something odd when he read the results of his observations. He realized that when Earth is closest to Jupiter, around early January, the Jupiter-Io eclipse interval becomes 11 minutes faster than the average interval. But when Earth is at its furthest from Jupiter, around mid-July, this interval turns out to be 11 minutes slower.
Roemer then thought that this difference in intervals was clearly not due to Io’s orbital period being unrelated to Jupiter’s relative position with respect to Earth. In other words, Io’s orbital period is constant, whether observed from Earth in January or July.
He then hypothesized that vision is not instantaneous. Consequently, the speed of light must be finite. This was against the consensus of the time; the speed of light is infinite. Roemer comes face to face with Rene Descartes, one of the advocates of the infinite speed of light.
Using Roemer’s data, the Dutch native Christiaan Huygens obtained an estimate of the speed of light, often called the constant c, using the following formula: if light from Io takes (11 + 11) minutes to travel once the diameter of Earth’s orbit, then c is equivalent to about 2.1 × 10^8 m/s. This constant differs from today’s c, which is 3 × 10^8 m/s.
The two main reasons for this difference are that the clocks used as references at that time were not as accurate as they are today. Instead of an 11-minute interval difference, modern clocks show an interval difference of less than 7 minutes. In addition, the inaccurate measurement of the diameter of the Earth’s orbit at that time also contributed to this inaccuracy.
Maybe the limited speed of light is what prompted Albert Einstein as a child to imagine riding a beam of light. In turn, as Stephen Hawking points out, it was imagination that led him to the greatest formula of the century: E = mc^2.
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